Discovery Worksheets - Properties of Shapes

1 Name Date SHAPE NAMES. Three- dimensional Figures or Space Figures Rectangular Prism Cylinder Cone Sphere Two- dimensional Figures or Plane Figures Square Rectangle Triangle Circle Name each shape. 1. 2. 3. 4. [triangle] [cone] [square] [sphere]. 5. 6. 7. 8. Discovery Education. All Rights Reserved. [rectangular prism] [circle] [cylinder] [rectangle]. 9. Which figures in the exercises are plane figures? [1, 3, 6, 8]. 10. Which figures in the exercises are space figures? [2, 4, 5, 7]. CHALLENGE. Name a real-life example of a rectangular prism, a cylinder, a cone, and a sphere. [Answers may vary. Possible answers: rectangular prism: cereal box;. cylinder: can of soup; cone: ice cream cone; sphere: ball]. LEVEL. 1. Discovering Math, Geometry, Shape , Get in Shape Name Date SHAPE NAMES. Three- dimensional Figures cube rectangular square sphere cylinder cone prism pyramid Polygons triangle rectangle square pentagon hexagon octagon Name each figure.

2 1. 2. 3. 4. Discovery Education. All Rights Reserved. [square pyramid] [cylinder] [pentagon] [triangle]. 5. 6. 7. 8. [rectangle] [sphere] [hexagon] [cone]. CHALLENGE. A polygon with four sides is called a quadrilateral. Draw a quadrilateral that is not a rectangle. Then draw another quadrilateral that is not a parallelogram and not a trapezoid. [Check students' drawings.]. LEVEL. 2. Discovering Math, Geometry, Shape , Get in Shape Name Date SHAPE NAMES. Polygons Triangle Quadrilateral Pentagon Hexagon Octagon 3 sides 4 sides 5 sides 6 sides 8 sides 3 angles 4 angles 5 angles 6 angles 8 angles Special Quadrilaterals Trapezoid Parallelogram Rectangle Rhombus Square Only two Opposite sides Parallelogram Parallelogram Rectangle with parallel sides. are parallel and with 4 right with all sides the all sides the the same length. angles. same length. same length.

3 Name each polygon. 1. 2. 3. 4. Discovery Education. All Rights Reserved. [pentagon] [octagon] [triangle] [hexagon]. Classify each quadrilateral. Some may have more than one name. 5. 6. 7. [parallelogram, [parallelogram, rectangle, rhombus] [trapezoid] rhombus, square]. LEVEL. 3. Discovering Math, Geometry, Shape , Get in Shape Name Date Properties OF GEOMETRIC FIGURES. Angles Right Angle Acute Angle Obtuse Angle A right angle forms a An acute angle is less than An obtuse angle is greater square corner. a right angle. than a right angle. The square in the corner means the angle is a right angle. Tell whether each angle is right, acute, or obtuse. 1. 2. 3. 4. [acute] [right] [obtuse] [acute]. Tell whether the angle each arrow points to is right, acute, or obtuse. Discovery Education. All Rights Reserved. 5. 6. CHALLENGE. Draw a triangle with an obtuse angle.

4 [Check students' drawings.]. LEVEL. 1. Discovering Math, Geometry, Properties of Geometric , Information in Forms Name Date Properties OF GEOMETRIC FIGURES. Angles Right Angle Acute Angle Obtuse Angle A right angle forms a An acute angle is less than An obtuse angle is greater square corner. a right angle. than a right angle. An angle can be named in three ways. B or ABC or CBA. Read: angle B or angle ABC or angle CBA. Two rays meet at an endpoint to form an angle. The endpoint is always included in the angle name. Tell whether each angle is right, acute, or obtuse. 1. 2. 3. 4. [acute] [right] [obtuse] [acute]. Discovery Education. All Rights Reserved. For each figure, tell whether ABC is right, acute, or obtuse. 5. 6. 7. 8. [right] [right] [obtuse] [obtuse]. CHALLENGE. Classify each of the angles of the parallelogram. [angles A and C are acute and angles B and D are obtuse].

5 LEVEL. 2. Discovering Math, Geometry, Properties of Geometric , Information in Forms Name Date Properties OF GEOMETRIC FIGURES. An angle is formed when two rays meet at the same endpoint, or vertex. The angle can be named by three letters or by its vertex: ray B or ABC or CBA. ray vertex Angles are measured in degrees ( ). Right Angle Acute Angle Obtuse Angle Straight Angle A right angle An acute angle is An obtuse angle is A straight angle measures 90 . greater than 0 greater than 90 measures 180 . and less than 90 . and less than 180 . Use the figure below. Tell whether 1. DCG 2. GDE. each angle is right, acute, obtuse, or straight. [right] [straight]. 3. CDE 4. CDG. [obtuse] [acute]. Discovery Education. All Rights Reserved. Use the figure below. Name as many 5. acute 6. obtuse examples of each type of angle as possible. [ QJK or KLS] [ JKR or RKL].

6 7. right 8. straight [ JQR or QRK or [ QRS]. KRS or RSL]. LEVEL. 3. Discovering Math, Geometry, Properties of Geometric , Information in Forms Name Date ALTERING Shapes . Shapes can be combined to make different Shapes can be divided to make different Shapes . Shapes . Dividing a rectangle along the diagonal Joining two squares makes a rectangle: makes two triangles: Name the Shapes used to make each figure. 1. 2. [square and 2 triangles] [rectangle and 2 triangles]. 3. 4. [square and triangle] [2 rectangles and 4 triangles]. Discovery Education. All Rights Reserved. 5. 6. [6 triangles] [3 rectangles]. CHALLENGE. Make a new shape by combining at least 3 different geometric Shapes . [Check students' drawings.]. LEVEL. 1. Discovering Math, Geometry, Altering , Shape Shifting Name Date ALTERING Shapes . Polygons can be combined to make Polygons can be divided to make different different polygons.

7 Polygons. Joining a square and two triangles makes Dividing a parallelogram along the a trapezoid: diagonal makes two triangles: Name the polygons used to make each figure. Then identify the figure. 1. 2. [rectangle and 2 triangles; hexagon] [triangle and trapezoid; parallelogram]. 3. 4. [4 triangles; pentagon] [2 parallelograms; hexagon]. Discovery Education. All Rights Reserved. 5. 6. [2 trapezoids; hexagon] [trapezoid, 2 rectangles, 2 triangles; octagon]. CHALLENGE. Make a new shape by combining at least 3 different polygons. [Check students' drawings.]. LEVEL. 2. Discovering Math, Geometry, Altering , Shape Shifting Name Date ALTERING Shapes . Polygons can be combined to make Polygons can be divided to make different different polygons. polygons. Joining two parallelograms can make a A hexagon can be divided into two hexagon: trapezoids: Name the polygons used to make each figure.

8 Then identify the figure. 1. 2. [5 triangles; pentagon] [trapezoid and 2 triangles; trapezoid]. 3. 4. [2 trapezoids and rectangle; octagon] [triangle and trapezoid; pentagon]. 5. 6. Discovery Education. All Rights Reserved. [4 triangles; rhombus] [4 triangles; parallelogram]. CHALLENGE [Check students' drawings. Sample answers shown.]. Make a pentagon by joining together 4 triangles. Make a hexagon by joining together 6 triangles. LEVEL. 3. Discovering Math, Geometry, Altering , Shape Shifting Name Date CONGRUENT AND SIMILAR Shapes . Congruent Figures Similar Figures These rectangles are congruent. These rectangles are similar. Congruent figures have the same shape Similar figures have the same shape but and the same size. not the same size. Are the figures congruent, similar, or neither? 1. 2. [similar] [congruent]. 3. 4. [congruent] [similar]. Discovery Education.

9 All Rights Reserved. 5. 6. [similar] [neither]. 7. 8. [congruent] [neither]. LEVEL. 1. Discovering Math, Geometry, Congruent and Similar , Same Difference Name Date CONGRUENT AND SIMILAR Shapes . Congruent Figures Similar Figures Congruent figures have Similar figures have the same shape and the same shape but the same size. not the same size. The rectangles are similar. The rectangles are congruent. Are the figures congruent, similar, or neither? 1. 2. [congruent] [similar]. 3. 4. Discovery Education. All Rights Reserved. [similar] [congruent]. 5. 6. [congruent] [neither]. CHALLENGE. Danny takes a photograph of his house. Then he has the photograph enlarged. Is the house in the enlargement congruent to the house in the original photograph? Is it similar? Explain. [It is not congruent because the enlargement is larger than the original. It is similar since everything should be enlarged by the same ratio.]

10 ]. LEVEL. 2. Discovering Math, Geometry, Congruent and Similar , Same Difference Name Date CONGRUENT AND SIMILAR Shapes . Similar Figures Congruent Figures Similar figures have Congruent figures have the same shape but the same shape not the same size. and the same size. The triangles are similar. The triangles are congruent. The corresponding angles of the triangles Since they are the same shape, are equal. The ratios of corresponding the triangles are also similar. The ratios of sides are equal. corresponding sides of the triangles is 1:1. Are the figures congruent, similar, neither, or both? 1. 2. [similar] [neither]. 3. 4. Discovery Education. All Rights Reserved. [both] [neither]. CHALLENGE. Draw a rectangle on the grid. Then draw a rectangle that is similar but not congruent to your rectangle. [Check students' drawings.]. Explain how you know the rectangles are similar.